Date Thesis Awarded

4-2019

Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)

Department

Interdisciplinary Studies

Advisor

Leah Shaw

Committee Members

Leah Shaw

Romuald Lipcius

Junping Shi

Abstract

Oysters have experienced drastic declines in their population because of environmental factors and harvesting pressures, making them a focal species for restoration eﬀorts [1, 22]. Oyster shell has become a limited resource and alternative substrates are not as suitable for larval recruitment and shell accumulation [1, 2, 7]. For this reason, restoration eﬀorts are restricted, despite the attempts in the private and public sector. To increase the eﬀectiveness of restoration, the dynamics of oyster reef systems must be further analyzed and understood. This thesis proposes a stage-structured ordinary diﬀerential equation model to investigate the dynamics of deterministic and stochastic oyster reef systems.

Our self-replenishing oyster model expands upon the JARS stage-structured ODE model of oyster populations and allows for larval production from the natal reef [31]. There are four compartments to the model - juvenile oysters, adult oysters, oyster shell volume, and sediment volume. In this research, we evaluate the bifurcation structures of a deterministic model with diﬀerent larval sources (internal and external). The deterministic stability analyses provide intuition into the overall structural dynamics of the equilibria of the system in response to changes in external (P0) and internal (P1) larval production.

Parameter sensitivity analysis is conducted with this deterministic model to evaluate the impact of the parameters important to our predictions for reef restoration. Based on the results and to ensure careful estimation, the parameters for instantaneous growth rate (φ) and natural mortality (µ) are estimated using ﬁeld data. Both of these parameters directly inﬂuence the change in adult oyster volume over time. The results of this section inform our understanding of the system dynamics in response to changes in parameters related to adult oyster growth and their ecosystem services.

To evaluate this system in the context of environmental changes, we introduce stochastic larval availability to the model. Tests of normality and variance are used to analyze the stochastic data. Additionally, we use autocorrelation function analysis to quantify ii the time delay we observed in the data across the four model compartments. Analysis of this stochastic model informs our understanding of the distribution of sample data in each compartment as a response to annual changes in larval availability.

The main implication of this work is to inform future oyster reef restoration eﬀorts. Critical reef height (Rc) is deﬁned as the minimum height the reef must initially be for the population to persist over time and is integral to restoration reef success. With the stochastic and deterministic models, Rc is determined. We vary the initial conditions of the Rc simulations to reﬂect common restoration strategies, in turn, producing biologically applicable results for reef restoration. Through this Rc analysis, and our understanding of the oyster reef system, predictions are made that can be experimentally tested in future work.

Recommended Citation

Wilson, Rachel, "A stage-structured oyster population model for reef restoration" (2019). Undergraduate Honors Theses. William & Mary. Paper 1403.
https://scholarworks.wm.edu/honorstheses/1403